Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
Exactly Solvable and Integrable Systems
2016-06-08 v1
Abstract
We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its B\"acklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of B\"acklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations we derive new vector Yang-Baxter map and integrable discrete vector sine-Gordon equation on a sphere.
Keywords
Cite
@article{arxiv.1507.07248,
title = {Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere},
author = {Alexander V. Mikhailov and Georgios Papamikos and Jing Ping Wang},
journal= {arXiv preprint arXiv:1507.07248},
year = {2016}
}